The 25-year-old joined the Citizens for £20 million last month but will be unable to make his debut for the club until August.
Guardiola suffered a knee injury during training and has been ruled out of the opening weeks of the Premier League season.
“I’m really excited, to be honest. I am very happy and glad to be here. It’s an honour and I’m looking forward to the new season,” Gundogan told the Daily Mail.
“It’s a great club. An incredible club and a big honour. It is my first time outside Germany so it will be a big adventure for me. I am really happy and cannot wait to play my first match in the stadium.
“I know (City boss Pep Guardiola) from Germany. I was lucky to play against him. He’s incredible.
“He’s one of the biggest managers in the world and history and we are all very lucky to have him here. We will have big achievements in the future.”
The 25-year-old playmaker provided seven assists and scored three goals in 40 appearances for Borussia Dortmund in all competitions last season.
Gundogan missed out on this summers Euro 2016 due to his knee injury. Germany have advanced to the semi finals of Euro 2016 after recording a win over Italy on penalties. Joachim Low’s side take on the hosts France in the semi-finals on Thursday evening.